User blog:Googleaarex/Dollar Function: final version FGH
This is FGH version of Dollar Function. Bracket Notation 1 has growth rate 0 (equal!) 0 has growth rate 1 (equal!), because n$0# = n$n# 1 has growth rate 2 (equal!), because @+1 = @...@. n has growth rate n+1 (equal!) 0 has growth rate w, because it nested. [10] has growth rate w+1, because # = #...#. [n0] has growth rate w+n [00] has growth rate w*2, because [0 #] = # [0...0] (n 0's) has growth rate w*n 1 has growth rate w^2 [1...1] (n 1's) has growth rate w^2*n 1 has growth rate w^3 n has growth rate w^{n+1} [0] has growth rate w^w [1] has growth rate w^w^2 [n] has growth rate w^w^{n+1} [[0]] has growth rate w^w^w [...0...] (n nested) has growth rate w^^{n-1} Extended Bracket Notation [02] has growth rate e(0), because f(02) = f([...f(0)...]). [n02] has growth rate e(0)+n [002] has growth rate e(0)+w [002] has growth rate e(0)+w^w [[...0...]02] (n nested) has growth rate e(0)+w^^n [[02]02] has growth rate e(0)*2 [[002]02] has growth rate e(0)*w [[[02]02]02] has growth rate e(0)^2 [[[[02]02]02]02] has growth rate e(0)^e(0) [[...[02]...]02] (n*2 nested) has growth rate e(0)^^n [[...[02]...]02] (n*2+1 nested) has growth rate e(0)^...^e(0)^2 (n e(0)'s) [0202] has growth rate e(1) [02...02] (n 02's) has growth rate e(n-1) [12] has growth rate e(w), because #@ = #@...#@. [02...0212] (n 02's) has growth rate e(w+n) [1212] has growth rate e(w*2) [12...12] (n 12's) has growth rate e(w*n) [22] has growth rate e(w^2) [n2] has growth rate e(w^n) [02] has growth rate e(w^w) [[...0...]2] (n nested) has growth rate e(w^^n) [[[02]]2] has growth rate e(e(0)) [[[[[02]]2]2] has growth rate e(e(e(0))) [[[...02]...]2] (n 2's) has growth rate e(...(e(0)...) (n nested) [[02]2] has growth rate z(0) [02[02]2] has growth rate e(z(0)+1) [12[02]2] has growth rate e(z(0)+w) [[[02]]2[02]2] has growth rate e(z(0)+e(0)) [[[[02]2]]2[02]2] has growth rate e(z(0)*2) [[02]2[02]2] has growth rate z(1) [[102]2] has growth rate z(w) [[[02]02]2] has growth rate z(e(0)) [[[[02]2]02]2] has growth rate z(z(0)) [[0202]2] has growth rate eta(0) [[12]2] has growth rate phi(w,0) [[[[02]]2]2] has growth rate phi(e(0),0) [[[02]2]2] has growth rate gamma(0) [[[0202]2]2] has growth rate phi(1,0,0,0) [[[02...02]2]2] (n 02's) has growth rate theta(W^n) [[[12]2]2] has growth rate SVO [[[n2]2]2] has growth rate theta(W^w^n) [[[02]2]2] has growth rate theta(W^w^w) [[[[[02]]2]2]2] has growth rate theta(W^e(0)) [[[[[[02]2]]2]2]2] has growth rate theta(W^gamma(0)) [[[[[[[02]2]2]]2]2]2] has growth rate theta(W^SVO) [[[[02]2]2]2] has growth rate LVO [[[[12]2]2]2] has growth rate theta(W^W^w) [[[[[02]2]2]2]2] has growth rate theta(W^W^W) [[...02]...]2] (n nested) has growth rate theta(W^^(n-2)) [03] has growth rate BHO, because f(0@+1) = f([...f(0@)...]@). [0303] has growth rate theta(e(W+1),1) [13] has growth rate theta(e(W+1),w) [[[02]]3] has growth rate theta(e(W+1),w) [[[03]]3] has growth rate theta(e(W+1),BHO) [[02]3] has growth rate theta(e(W+1)+1) [[[02]2]3] has growth rate theta(e(W+1)+W) [[[[02]2]2]3] has growth rate theta(e(W+1)+W^W) [[[03]2]3] has growth rate theta(e(W+1)*2) [[03]3] has growth rate theta(z(W+1)) [[13]3] has growth rate theta(phi(w,W+1)) [[[02]3]3] has growth rate theta(phi(W,1)) [[[03]3]3] has growth rate theta(W_2) [[[[03]3]3]3] has growth rate theta(W_2^W_2) [04] has growth rate theta(e(W_2+1)) [[04]4] has growth rate theta(z(W_2+1)) [[[04]4]4] has growth rate theta(W_3) [0n] has growth rate theta(e(W_{n-2}+1)) [00] has growth rate theta(W_w) [010] has growth rate TBF [0n0] has growth rate theta(e(W_{w+n-1}+1)) [000] has growth rate theta(W_{w*2}) [00...0] (n 0's) has growth rate theta(W_{w*n}) [01] has growth rate theta(W_w^2) [0n] has growth rate theta(W_w^{n+1}) [00] has growth rate theta(W_w^w) [0[02]] has growth rate theta(W_e(0)) [0[03]] has growth rate theta(W_BHO) [0[0n]] has growth rate theta(W_theta(e(W_{n-2}+1))) [0[00]] has growth rate theta(W_theta(W_w)) [0[...00...]] (n subscripts) has growth rate theta(W_...theta(W_w)...) (n W's) [002] has growth rate theta(W_W) [002...02] (n 02's) has growth rate theta(W_{W*n}) [012] has growth rate theta(W_{W*w}) [0[02]2] has growth rate theta(W_W^2) [003] has growth rate theta(W_e(W+1)) [000] has growth rate theta(W_W_w) [0...0] (n 0's) has growth rate theta(W_..._w) (n-1 W's) Linear Array Notation [[0,1]] has growth rate psi(psi_I(0)) [[0...0,1]] (n 0's) has growth rate psi(psi_I(n-1)) [[1,1]] has growth rate psi(psi_I(w)) [[02,1]] has growth rate psi(psi_I(W)) [[03,1]] has growth rate psi(psi_I(e(W+1))) [[00,1]] has growth rate psi(psi_I(W_w)) [[000,1]] has growth rate psi(psi_I(W_W_w)) [[[0,1],1]] has growth rate psi(psi_I(psi_I(0))) [[0,12,1]] has growth rate psi(psi_I(I)) [[[0,1]0,12,1]] has growth rate psi(psi_I(I+psi_I(0))) [[0,120,12,1]] has growth rate psi(psi_I(I*2)) [[0,12...0,12,1]] (n 0,12's) has growth rate psi(psi_I(I*n)) [[1,12,1]] has growth rate psi(psi_I(I*w)) [[[02,1]2,1]] has growth rate psi(psi_I(I*W)) [[[00,1]2,1]] has growth rate psi(psi_I(I*W_w)) [[[0,1],1]2,1]] has growth rate psi(psi_I(I*psi_I(0))) [[0,12,1]2,1]] has growth rate psi(psi_I(I^2)) [[[0,12,1]2,1]2,1]] has growth rate psi(psi_I(I^I)) [[0,13,1]] has growth rate psi(psi_I(e(I+1))) [[0,120,13,1]] has growth rate psi(psi_I(e(I+1)+I)) [[[0,13,1]20,13,1]] has growth rate psi(psi_I(e(I+1)*2)) [[0,130,13,1]] has growth rate psi(psi_I(e(I+2))) [[1,13,1]] has growth rate psi(psi_I(e(I+w))) [[[02,1]3,1]] has growth rate psi(psi_I(e(I+W))) [[[0,12,1]3,1]] has growth rate psi(psi_I(e(I*2))) [[[[02,1]2,1]3,1]] has growth rate psi(psi_I(e(I*W))) [[[[0,12,1]2,1]3,1]] has growth rate psi(psi_I(e(I^2))) [[[[0,13,1]2,1]3,1]] has growth rate psi(psi_I(e(e(I+1)))) [[[0,13,1]3,1]] has growth rate psi(psi_I(z(I+1))) or psi(psi_I(theta_{I+1}(2))) [[[0,130,13,1]3,1]] has growth rate psi(psi_I(eta(I+1))) or psi(psi_I(theta_{I+1}(3))) [[[1,13,1]3,1]] has growth rate psi(psi_I(phi(w,I+1))) or psi(psi_I(theta_{I+1}(w))) [[[[02,1]3,1]3,1]] has growth rate psi(psi_I(phi(W,I+1))) or psi(psi_I(theta_{I+1}(W))) [[[[00,1]3,1]3,1]] has growth rate psi(psi_I(phi(W,I+1))) or psi(psi_I(theta_{I+1}(W_w))) [[[[[0,1],1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(0)))) [[[[[0,12,1],1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(I)))) [[[[[0,13,1],1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(e(I+1))))) [[[[0,12,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(I))) [[[[[0,13,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(e(I+1)))) [[[[[[0,13,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(e(I+1)))) [[[[[[1,13,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(w)))) [[[[[[[02,1]3,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(W)))) [[[[[[[[0,1],1]3,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(psi_I(0))))) [[[[[[[0,12,1]3,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(I)))) [[[[[[[[[[0,12,1]3,1]3,1]2,1]3,1]3,1]2,1]3,1]3,1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(theta_{I+1}(I))))) [[[[0,13,1]3,1]3,1]] has growth rate psi(psi_I(W_{I+1})) [[[[[0,13,1]3,1]3,1]3,1]] has growth rate psi(psi_I(W_{I+1}^W_{I+1})) [[0,14,1]] has growth rate psi(psi_I(e(W_{I+1}))) [[0,1n,1]] has growth rate psi(psi_I(e(W_{I+n-3}))) [[0,10,1]] has growth rate psi(psi_I(W_{I+w})) [[0,102,1]] has growth rate psi(psi_I(W_{I+W})) [[0,100,1]] has growth rate psi(psi_I(W_{I+W_w})) [[0,1[0,1],1]] has growth rate psi(psi_I(W_{I+psi_I(0)})) [[0,1[0,12,1],1]] has growth rate psi(psi_I(W_{I+psi_I(I)})) [[0,1[0,1n,1],1]] has growth rate psi(psi_I(W_{I+psi_I(e(W_{I+n-3}))})) [[0,1[0,10,1],1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+w})})) [[0,1[0,1[0,1],1],1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(0)})})) [[0,1[0,1[0,10,1],1],1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(W_{I+w})})})) [[0,1[0,1[0,1[0,1],1],1],1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(W_{I+psi_I(0)})})})) [[0,10,12,1]] has growth rate psi(psi_I(W_{I*2})) [[0,10,12...0,12,1]] (n 0,12's) has growth rate psi(psi_I(W_{I*(n+1)})) [[0,1n,12,1]] has growth rate psi(psi_I(W_{I*w^n})) [[0,1[0,12,1]2,1]] has growth rate psi(psi_I(W_{I^2})) [[0,10,12[0,12,1]2,1]] has growth rate psi(psi_I(W_{I^2+I})) [[0,1[0,12,1]2[0,12,1]2,1]] has growth rate psi(psi_I(W_{I^2*2})) [[0,1[10,12,1]2,1]] has growth rate psi(psi_I(W_{I^2*w})) [[0,1[0,120,12,1]2,1]] has growth rate psi(psi_I(W_{I^3})) [[0,1[1,12,1]2,1]] has growth rate psi(psi_I(W_{I^w})) [[0,1[[0,12,1]2,1]2,1]] has growth rate psi(psi_I(W_{I^I})) [[0,1[0,13,1]2,1]] has growth rate psi(psi_I(W_e(I+1))) [[0,1[[0,13,1]3,1]2,1]] has growth rate psi(psi_I(W_theta_{I+1}(2))) [[0,1[[[0,12,1]3,1]3,1]2,1]] has growth rate psi(psi_I(W_theta_{I+1}(I))) [[0,1[[[0,13,1]3,1]3,1]2,1]] has growth rate psi(psi_I(W_theta_{I+1}(W_{I+1}))) [[0,1[0,14,1]2,1]] has growth rate psi(psi_I(W_theta_{I+1}(e(W_{I+1}+1)))) [[0,1[0,10,1]2,1]] has growth rate psi(psi_I(W_theta_{I+1}(W_{I+w}))) [[0,10,13,1]] has growth rate psi(psi_I(W_W_{I+1})) [[0,10,10,1]] has growth rate psi(psi_I(W_W_{I+w})) [[0,10,1[0,1],1]] has growth rate psi(psi_I(W_W_{I+psi_I(0)})) [[0,10,10,12,1]] has growth rate psi(psi_I(W_W_{I*2})) [[0,2]] has growth rate psi(psi_{I_2}(0)) [[0,12,2]] has growth rate psi(psi_{I_2}(I)) [[0,22,2]] has growth rate psi(psi_{I_2}(I_2)) [[0,220,22,2]] has growth rate psi(psi_{I_2}(I_2*2)) [[1,22,2]] has growth rate psi(psi_{I_2}(I_2*w)) [[[02,2]2,2]] has growth rate psi(psi_{I_2}(I_2*W)) [[[0,12,2]2,2]] has growth rate psi(psi_{I_2}(I_2*I)) [[[0,22,2]2,2]] has growth rate psi(psi_{I_2}(I_2^2)) [[0,23,2]] has growth rate psi(psi_{I_2}(e(I_2+1))) [[0,20,2]] has growth rate psi(psi_{I_2}(W_{I_2+w})) [[0,202,2]] has growth rate psi(psi_{I_2}(W_{I_2+W})) [[0,20,12,2]] has growth rate psi(psi_{I_2}(W_{I_2+I})) [[0,20,22,2]] has growth rate psi(psi_{I_2}(W_{I_2*2})) [[0,20,20,2]] has growth rate psi(psi_{I_2}(W_W_{I_2+w})) [[0,20,20,12,2]] has growth rate psi(psi_{I_2}(W_W_{I_2+I})) [[0,20,20,22,2]] has growth rate psi(psi_{I_2}(W_W_{I_2*2})) [[0,3]] has growth rate psi(psi_{I_3}(0)) [[0,n]] has growth rate psi(psi_{I_n}(0)) [[0,0]] has growth rate psi(psi_{I_w}(0)) [[0,02]] has growth rate psi(psi_{I_W}(0)) [[0,0,12]]] has growth rate psi(psi_{I_I}(0)) [[0,[0,0]]] has growth rate psi(psi_{I_I_w}(0)) [[0,0,12]] has growth rate psi(psi_{I(1,0)}(0)) [[0,0,120,12]] has growth rate psi(psi_{I(1,0)}(1)) [[0,1,12]] has growth rate psi(psi_{I(1,0)}(w)) [[0,[[0,1],1]2]] has growth rate psi(psi_{I(1,0)}(psi_I(0))) [[0,[0,0]2]] has growth rate psi(psi_{I(1,0)}(I_w)) [[0,[0,0,12]2]] has growth rate psi(psi_{I(1,0)}(I(1,0))) I don't know of limit growth rate of linear array notation. I predict psi(psi_{Xi(w,0)}(0)). So, can you convert Dollar Function to FGH? Dimensional Arrays [[0(1)1]] has growth rate psi(psi_{Xi(w,0)}(0)) [[[0(1)1](1)1]] has growth rate psi(psi_{Xi(Xi(w,0),0)}(0)) [[0(1)12(1)1]] has growth rate psi(psi_{Xi(K,0)}(0)) [[0(1)120(1)12(1)1]] has growth rate psi(psi_{Xi(K*2,0)}(0)) [[0(1)13(1)1]] has growth rate psi(psi_{Xi(e(K+1),0)}(0)) [[0,1(1)1]] has growth rate psi(psi_{W(W{2}^3+W{2})}(0)) [[0(1)2]] has growth rate psi(psi_{W(W{2}^3*2)}(0)) [[0(1)0,1]] has growth rate psi(psi_{W(W{2}^4)}(0)) [[0(1)0(1)1]] has growth rate psi(psi_{W(W{2}^w)}(0)) [[0(2)1]] has growth rate psi(psi_{W(W{2}^W{2}^w)}(0)) [[0(0)1]] has growth rate psi(psi_{W(W{2}^W{2}^W{2}^w)}(0)) Nested Array Notation [[0(0,1)1]] has growth rate psi(psi_{W(e(W{2}+1))}(0)) Hyper-Nested Array Notation Category:Blog posts